Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis Calculator

✖Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola.ⓘ Semi Conjugate Axis of Hyperbola [b]			+10% -10%
✖Eccentricity of Hyperbola is the ratio of distances of any point on the Hyperbola from focus and the directrix, or it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola.ⓘ Eccentricity of Hyperbola [e]			+10% -10%

✖Focal Parameter of Hyperbola is the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola.ⓘ Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis [p]

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Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola/(Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1))
p = b/(e/sqrt(e^2-1))
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Focal Parameter of Hyperbola - (Measured in Meter) - Focal Parameter of Hyperbola is the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola.
Semi Conjugate Axis of Hyperbola - (Measured in Meter) - Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola.
Eccentricity of Hyperbola - (Measured in Meter) - Eccentricity of Hyperbola is the ratio of distances of any point on the Hyperbola from focus and the directrix, or it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola.

STEP 1: Convert Input(s) to Base Unit

Semi Conjugate Axis of Hyperbola: 12 Meter --> 12 Meter No Conversion Required
Eccentricity of Hyperbola: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p = b/(e/sqrt(e^2-1)) --> 12/(3/sqrt(3^2-1))

Evaluating ... ...

p = 11.3137084989848

STEP 3: Convert Result to Output's Unit

11.3137084989848 Meter --> No Conversion Required

FINAL ANSWER

11.3137084989848 ≈ 11.31371 Meter <-- Focal Parameter of Hyperbola

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Focal Parameter of Hyperbola Calculators

Focal Parameter of Hyperbola

LaTeX Go Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)

Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis

LaTeX Go Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola/(Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1))

Focal Parameter of Hyperbola given Linear Eccentricity and Semi Transverse Axis

LaTeX Go Focal Parameter of Hyperbola = (Linear Eccentricity of Hyperbola^2-Semi Transverse Axis of Hyperbola^2)/Linear Eccentricity of Hyperbola

Focal Parameter of Hyperbola given Linear Eccentricity and Semi Conjugate Axis

LaTeX Go Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/Linear Eccentricity of Hyperbola

Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis Formula

LaTeX Go

Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola/(Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1))
p = b/(e/sqrt(e^2-1))

What is Hyperbola?

A Hyperbola is a type of conic section, which is a geometric figure that results from intersecting a cone with a plane. A Hyperbola is defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is constant. In other words, a Hyperbola is the locus of points where the difference between the distances to two fixed points is a constant value. The standard form of the equation for a Hyperbola is: (x - h)²/a² - (y - k)²/b² = 1

What is Focal Parameter of a Hyperbola and how is it calculated?

The focal parameter of the Hyperbola is the shortest distance from a focus to the corresponding directrix. It is calculated by the formula p= b²/√(a²+b²) where p is the focal parameter of the Hyperbola, b is the semi conjugate axis of the Hyperbola and a is the semi transverse axis of the Hyperbola.

How to Calculate Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis?

Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis calculator uses Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola/(Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1)) to calculate the Focal Parameter of Hyperbola, The Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola. Focal Parameter of Hyperbola is denoted by p symbol.

How to calculate Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis using this online calculator? To use this online calculator for Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis, enter Semi Conjugate Axis of Hyperbola (b) & Eccentricity of Hyperbola (e) and hit the calculate button. Here is how the Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis calculation can be explained with given input values -> 11.31371 = 12/(3/sqrt(3^2-1)).

FAQ

What is Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis?

The Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola and is represented as p = b/(e/sqrt(e^2-1)) or Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola/(Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1)). Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola & Eccentricity of Hyperbola is the ratio of distances of any point on the Hyperbola from focus and the directrix, or it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola.

How to calculate Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis?

The Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola is calculated using Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola/(Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1)). To calculate Focal Parameter of Hyperbola given Eccentricity and Semi Conjugate Axis, you need Semi Conjugate Axis of Hyperbola (b) & Eccentricity of Hyperbola (e). With our tool, you need to enter the respective value for Semi Conjugate Axis of Hyperbola & Eccentricity of Hyperbola and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Focal Parameter of Hyperbola?

In this formula, Focal Parameter of Hyperbola uses Semi Conjugate Axis of Hyperbola & Eccentricity of Hyperbola. We can use 3 other way(s) to calculate the same, which is/are as follows -

Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)
Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/Linear Eccentricity of Hyperbola
Focal Parameter of Hyperbola = (Linear Eccentricity of Hyperbola^2-Semi Transverse Axis of Hyperbola^2)/Linear Eccentricity of Hyperbola

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